Effects of bidirectional shaking on nonlinear site response analysis

The current practice of site response analysis (SRA) usually uses unidirectional (1D) input shaking, even though earthquake motions are multidirectional in nature. Past research has shown that shaking in two simultaneous orthogonal horizontal directions, referred to as bidirectional (2D) shaking, leads to larger soil shear strains and hysteretic response than 1D shaking. However, those studies used limited ground motions and site conditions and did not account for ground motion directionality. This study examines the effects of 2D shaking on nonlinear SRA based on a large number of ground motions at multiple hazard levels, dense dry sandy soil profiles with different elastic site periods ( Ts ), and ground motion directionality. The nonlinear SRAs were performed using 3D soil column models in LS-DYNA with hysteretic soil constitutive models (MAT_079 and I-soil) that consider multidimensional stress states. The results showed that 2D shaking produced larger shear strains in the soil column, increasing the soil hysteretic damping and reducing the spectral acceleration ( Sa ) at the ground surface. This effect was mainly observed at periods below Ts but could extend to periods above Ts due to period elongation as a result of soil nonlinearity. Moreover, the differences between Sa at the soil surface from 2D and 1D shaking were strongly correlated with the peak ground acceleration of the base motions. The difference between 1D and 2D SRA in terms of Sa was not influenced by ground motion directionality for a large set of polarized motions but did show some notable differences for individual motions. These numerical results illustrate conditions when performing nonlinear SRA with 2D shaking will benefit over 1D shaking. The findings can be used to reduce the epistemic uncertainty in SRA and improve the current SRA practice.